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Simplifying 135 + -1(6x + 14) = 6(x + 5) * x Reorder the terms: 135 + -1(14 + 6x) = 6(x + 5) * x 135 + (14 * -1 + 6x * -1) = 6(x + 5) * x 135 + (-14 + -6x) = 6(x + 5) * x Combine like terms: 135 + -14 = 121 121 + -6x = 6(x + 5) * x Reorder the terms: 121 + -6x = 6(5 + x) * x Reorder the terms for easier multiplication: 121 + -6x = 6x(5 + x) 121 + -6x = (5 * 6x + x * 6x) 121 + -6x = (30x + 6x2) Solving 121 + -6x = 30x + 6x2 Solving for variable 'x'. Combine like terms: -6x + -30x = -36x 121 + -36x + -6x2 = 30x + 6x2 + -30x + -6x2 Reorder the terms: 121 + -36x + -6x2 = 30x + -30x + 6x2 + -6x2 Combine like terms: 30x + -30x = 0 121 + -36x + -6x2 = 0 + 6x2 + -6x2 121 + -36x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 121 + -36x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -20.16666667 + 6x + x2 = 0 Move the constant term to the right: Add '20.16666667' to each side of the equation. -20.16666667 + 6x + 20.16666667 + x2 = 0 + 20.16666667 Reorder the terms: -20.16666667 + 20.16666667 + 6x + x2 = 0 + 20.16666667 Combine like terms: -20.16666667 + 20.16666667 = 0.00000000 0.00000000 + 6x + x2 = 0 + 20.16666667 6x + x2 = 0 + 20.16666667 Combine like terms: 0 + 20.16666667 = 20.16666667 6x + x2 = 20.16666667 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 20.16666667 + 9 Reorder the terms: 9 + 6x + x2 = 20.16666667 + 9 Combine like terms: 20.16666667 + 9 = 29.16666667 9 + 6x + x2 = 29.16666667 Factor a perfect square on the left side: (x + 3)(x + 3) = 29.16666667 Calculate the square root of the right side: 5.400617249 Break this problem into two subproblems by setting (x + 3) equal to 5.400617249 and -5.400617249.Subproblem 1
x + 3 = 5.400617249 Simplifying x + 3 = 5.400617249 Reorder the terms: 3 + x = 5.400617249 Solving 3 + x = 5.400617249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 5.400617249 + -3 Combine like terms: 3 + -3 = 0 0 + x = 5.400617249 + -3 x = 5.400617249 + -3 Combine like terms: 5.400617249 + -3 = 2.400617249 x = 2.400617249 Simplifying x = 2.400617249Subproblem 2
x + 3 = -5.400617249 Simplifying x + 3 = -5.400617249 Reorder the terms: 3 + x = -5.400617249 Solving 3 + x = -5.400617249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -5.400617249 + -3 Combine like terms: 3 + -3 = 0 0 + x = -5.400617249 + -3 x = -5.400617249 + -3 Combine like terms: -5.400617249 + -3 = -8.400617249 x = -8.400617249 Simplifying x = -8.400617249Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.400617249, -8.400617249}
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